Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

Abstract

Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number $N_f$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED${}_3$) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal QED${}_3$ phase and a confining valence-bond-solid phase with spontaneously broken point-group symmetries. The critical continuum theory of this transition was shown to be the $O(2)$ QED${}_3$-Gross-Neveu model, equivalent to the gauged Nambu-Jona-Lasinio model, and critical exponents were computed to first order in the large-$N_f$ expansion and the $\epsilon$ expansion. We extend these studies by computing critical exponents to second order in the large-$N_f$ expansion and to four-loop order in the $\epsilon$ expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete ${\mathbb{Z}}_4$ symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous $O(2)$ symmetry at criticality for all values of $N_f$.

arXiv comment16 pages, 6 figures, 8 tables; v2: published version

References in corpus (51)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Computational Studies of Quantum Spin Systems
• The Flux-Phase of the Half-Filled Band
• Algebraic spin liquid as the mother of many competing orders
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Fermion-induced quantum critical points
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Non-Compact QED_3 with N_f=1 and N_f=4
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Non-compact QED_3 with N_f >=2
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Scale-invariance of parity-invariant three-dimensional QED
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• Quantum Electrodynamics in d=3 from the epsilon-expansion
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
• Notes on Spinning Operators in Fermionic CFT
• Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics
• Anomalous dimensions of scalar operators in $QE{D}_3$
• Gauge-field-assisted Kekulé quantum criticality
• Computation of Critical Exponent Eta at O(1/N_f^2) in Quantum Electrodynamics in Arbitrary Dimensions
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
• Deconfined criticality in the QED${}_3$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited
• Large $N_f$ quantum field theory
• Emergent gauge fields and the high temperature superconductors
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• The Nambu-Jona-Lasinio Model at O(1/N^2)
• Deconfined criticality from the QED${}_3$-Gross-Neveu model at three loops
• Erratum: algebraic spin liquid as the mother of many competing orders
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Mott transition in the $\pi$-flux SU($4$) Hubbard model on a square lattice
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• The Beta-Function of the Chiral Gross Neveu Model at O(1/N^2)
• Transition between algebraic and ${\mathbb{Z}}_2$ quantum spin liquids at large $N$
• Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Chiral Symmetry breaking in Three Dimensional QED
• Critical properties of the Néel/algebraic-spin-liquid transition
• The abelian gauge-Yukawa $\beta$-functions at large $N_f$
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Gauge Independent Critical Exponents for QED Coupled to a Four Fermi Interaction with and without a Chern Simons Term
• Analysis of Abelian Gauge Theory with Four Fermi Interaction at $O(1/N^2)$ in Arbitrary Dimensions
• Gauged Nambu-Jona-Lasinio Model at O(1/N) with and without a Chern-Simons Term

Cited by in corpus (14)

• Quantum phase transitions in Dirac fermion systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• General scalar renormalisation group equations at three-loop order
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Symmetry-breaking effects of instantons in parton gauge theories
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Critical exponents for the valence-bond-solid transition in lattice quantum electrodynamics
• Quantum-critical electrodynamics of Luttinger fermions
• Critical structure and emergent symmetry of Dirac fermion systems
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Fermionic criticality with enlarged fluctuations in Dirac semimetals